6.2 Bayes’ Rule in practice: the likelihood ratio
In law, probabilities based on Bayes’ Rule are often presented in a particular form, known as the ‘likelihood ratio’. This is to avoid the legal requirement introduced earlier in the course that prevents experts from providing assistance on any non-expert issues. The likelihood ratio is a way of presenting probabilities in a way that does not depend on the probabilities of the rest of the evidence.
A likelihood ratio is calculated from a probability by dividing the probability by its opposite. For example, if the probability that it is going to rain on a certain day is 0.33, then the opposite is that there is a 0.66 probability that it is not going to rain. The likelihood ratio is, therefore, 0.33/0.66 = 0.5.
Whereas probabilities can take any value from 0 to 1, likelihood ratios can take any value from 0 to infinity. Likelihood ratios are not very intuitive, so you can refer to Table 2, which compares some probabilities with common likelihood ratios.
Table 2 Likelihood ratios
| Probability | Equivalent likelihood ratio | Verbal description |
|---|---|---|
| 0 | 0 | Impossible |
| 0.25 | 0.33 | |
| 0.5 | 1 | Evenly balanced |
| 0.75 | 3 | |
| 1 | Infinity | Certainty |
Table 3 shows likelihood ratios with categories of verbal equivalents used by the Association of Forensic Science Providers (AFSP) and adopted by a large number of forensic practitioners.
Table 3 Likelihood ratio scale suggested by the AFSP
| Value of likelihood ratio | Verbal equivalent |
|---|---|
| >1–10 | Weak support for proposition |
| 10–100 | Moderate support for proposition |
| 100–1000 | Moderately strong support for proposition |
| 1000–10,000 | Strong support for proposition |
| 10,000–1,000,000 | Very strong support for proposition |
| >1,000,000 | Extremely strong support for proposition |
In the next activity, you will see how different probabilities can be converted to likelihood ratios so that standard evidence and expert evidence can be combined.
Activity 7 Try your hand at using likelihood ratios
OpenLearn - Expert evidence and forensic science in the courtroom 
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